In this paper the definition of domination is generalized to the case that the elements of the traffic matrices may have negative values. It is proved that D_{3} dominates D_{3} + λ(D_{2} -D_{1}) for any λ > 0 if D_{1} dominates D_{2}. Let U(D) be the set of all the traffic matrices that are dominated by the traffic matrix D. It is shown that U(D_{∞}) and U(D_{∈}) are isomorphic. Besides, similar results are obtained on multi-commodity flow problems. Furthermore, the results are the generalized to integral flows.
We consider the boundary blow up problem for k-hessian equation with nonlinearities of power and of exponential type, and prove their existence, uniqueness and asymptotic behaviour. Moreover we also show that their perturbed problem has a unique positive solution, which satisfies some asymptotic behaviors to unperturbed problems under appropriate structure hypotheses for perturbed terms.
In this paper, the existence of a uniform exponential attractor for a second order non-autonomous lattice dynamical system with quasiperiodic symbols acting on a closed bounded set is considered. Firstly, the existence and uniqueness of solutions for the considered systems which generate a family of continuous processes is shown, and the existence of a uniform bounded absorbing sets for the processes is proved. Secondly, a semigroup defined on a extended space is introduced, and the Lipschitz continuity, α-contraction and squeezing property of this semigroup are proved. Finally, the existence of a uniform exponential attractor for the family of processes associated with the studied lattice dynamical systems is obtained.
A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, we verify the total coloring conjecture for every 1-planar graph G if either △(G) ≥ 9 and g(G) ≥ 4, or △(G) ≥ 7 and g(G) ≥ 5, where △(G) is the maximum degree of G and g(G) is the girth of G.
Detection of multiple outliers or subset of influential points has been rarely considered in the linear measurement error models. In this paper a new influence statistic for one or a set of observations is generalized and characterized based on the corrected likelihood in the linear measurement error models. This influence statistic can be expressed in terms of the residuals and the leverages of linear measurement error regression. Unlike Cook's statistic, this new measure of influence has asymptotically normal distribution and is able to detect a subset of high leverage outliers which is not identified by Cook's statistic. As an illustrative example, simulation studies and a real data set are analysed.
This paper considers a novel formulation of the multi-period network interdiction problem. In this model, delivery of the maximum flow as well as the act of interdiction happens over several periods, while the budget of resource for interdiction is limit. It is assumed that when an edge is interdicted in a period, the evader considers a rate of risk of detection at consequent periods. Application of the generalized Benders decomposition algorithm considers solving the resulting mixed-integer nonlinear programming problem. Computational experiences denote reasonable consistency with expectations.
Assuming that the failure time under different risk factors follows the independent exponential distribution, a joint model under Type-I hybrid censoring is addressed in detail. Based on the Maximum likelihood estimates (MLEs) of unknown parameters, we obtain exact distributions of MLEs by using the moment generating function (MGF). Confidence intervals (CIs) of parameters are constructed through both the exact method and the parametric bootstrap method. Then we compare the performances of different methods by Monte Carlo simulations. Finally, the validity of the proposed models and methods are demonstrated by a numerical example.
We investigate the Chapman-Jouguet model in multi-dimensional space, and construct explicitly its non-selfsimilar Riemann solutions. By the method we apply in this paper, general initial discontinuities can be dealt with, even for complex interaction of combustion waves. Furthermore, we analyze the way in which the area of unburnt gas shrinks.
In this paper, we consider the logarithmically improved regularity criterion for the supercritical quasi-geostrophic equation in Besov space Ḃ_{∞,∞}^{-r}(R^{2}).The result shows that if θ is a weak solutions satisfies ∫_{0}^{T}((‖▽θ(.,s)‖_{Ḃ∞,∞-r}^{(α/(α-r))})/(1+ln(e+‖▽┴θ(.,s)‖_{L}^{(2/r)}))ds<_{∞} for some 0 < r < α and 0 < α < 1, then θ is regular at t=T. In view of the embedding L^{(2/r)}⊂M_{(2/r)}^{p}⊂Ḃ_{∞,∞}^{-r} with 2 ≤ p < (2/r) and 0 ≤ r < 1, we see that our result extends the results due to[20] and[31].
We propose an inexact Newton method with a filter line search algorithm for nonconvex equality constrained optimization. Inexact Newton's methods are needed for large-scale applications which the iteration matrix cannot be explicitly formed or factored. We incorporate inexact Newton strategies in filter line search, yielding algorithm that can ensure global convergence. An analysis of the global behavior of the algorithm and numerical results on a collection of test problems are presented.
The lowest order H^{1}-Galerkin mixed finite element method (for short MFEM) is proposed for a class of nonlinear sine-Gordon equations with the simplest bilinear rectangular element and zero order RaviartThomas element. Base on the interpolation operator instead of the traditional Ritz projection operator which is an indispensable tool in the traditional FEM analysis, together with mean-value technique and high accuracy analysis, the superclose properties of order O(h^{2})/O(h^{2} + τ^{2}) in H^{1}-norm and H(div; Ω)-norm are deduced for the semi-discrete and the fully-discrete schemes, where h, τ denote the mesh size and the time step, respectively, which improve the results in the previous literature.
Let G be a graph embeddable in a surface of nonnegative characteristic with maximum degree six. In this paper, we prove that if G contains no a vertex v which is contained in all cycles of lengths from 3 to 6, then G is of Class 1.
This paper studies an M-estimator of a proxy periodic GARCH (p, q) scaling model and establishes its consistency and asymptotic normality. Simulation studies are carried out to assess the performance of the estimator. The numerical results show that our M-estimator is more efficient and robust than other estimators without the use of high-frequency data.
This work develops asymptotic expansions of systems of partial differential equations associated with multi-scale switching diffusions. The switching process is modeled by using an inhomogeneous continuoustime Markov chain. In the model, there are two small parameters ε and δ. The first one highlights the fast switching, whereas the other delineates the slow diffusion. Assuming that ε and δ are related in that ε=δγ, our results reveal that different values of γ lead to different behaviors of the underlying systems, resulting in different asymptotic expansions. Although our motivation comes from stochastic problems, the approach is mainly analytic and is constructive. The asymptotic series are rigorously justified with error bounds provided. An example is provided to demonstrate the results.
Robust image recovery methods have been attracted more and more attention in recent decades for its good property of tolerating system errors or measuring noise. In this paper, we propose a new robust method (ESL-SELO) to recover nosing image, which combine exponential loss function and seamless-L0 (SELO) penalty function to guarantee both accuracy and robustness of the estimator. Theoretical result showed that our method has a local optimal solution and good asymptotic properties. Finally, we compare our method with other methods in simulation which shows better robustness and takes much less time.
In this paper we present an infeasible-interior-point algorithm, based on a new wide neighbourhood N(τ_{1}, τ_{2}, η), for linear programming over symmetric cones. We treat the classical Newton direction as the sum of two other directions. We prove that if these two directions are equipped with different and appropriate step sizes, then the new algorithm has a polynomial convergence for the commutative class of search directions. In particular, the complexity bound is O(r^{1.5} log ε^{-1}) for the Nesterov-Todd (NT) direction, and O(r^{2} log ε^{-1}) for the xs and sx directions, where r is the rank of the associated Euclidean Jordan algebra and ε > 0 is the required precision. If starting with a feasible point (x^{0}, y^{0}, s^{0}) in N(τ_{1}, τ_{2}, η), the complexity bound is O(√r log ε^{-1}) for the NT direction, and O(r log ε^{-1}) for the xs and sx directions. When the NT search direction is used, we get the best complexity bound of wide neighborhood interior-point algorithm for linear programming over symmetric cones.
A weighted graph is a graph in which every edge is assigned a non-negative real number. In a weighted graph, the weight of a path is the sum of the weights of its edges, and the weighed degree of a vertex is the sum of the weights of the edges incident with it. In this paper we give three weighted degree conditions for the existence of heavy or Hamilton paths with one or two given end-vertices in 2-connected weighted graphs.
Chemotaxis is a type of oriented movement of cells in response to the concentration gradient of chemical substances in their environment. We consider local existence and stability of nontrivial steady states of a logistic type of chemotaxis. We carry out the bifurcation theory to obtain the local existence of the steady state and apply the expansion method on the chemotaxis to investigate the bifurcation direction. Moreover, by applying the bifurcation direction, we obtain the bifurcating steady state is stable when the bifurcation curve turns to right under certain conditions.
In this paper, we are interested in exploring the dynamic causal relationships among two sets of three variables in different quarters. One set is futures sugar closing price in Zhengzhou futures exchange market (ZC), spot sugar price in Zhengzhou (ZS) and futures sugar closing price in New York futures exchange market(NC) and the other includes futures sugar opening price in Zhengzhou (ZO), ZS and NC. For each quarter, we first use Bayesian model selection to obtain the optimal causal graph with the highest BD scores and then use Bayesian model averaging approach to explore the causal relationship between every two variables. From the real data analysis, the two conclusions almost coincide, which shows that the two methods are practical.
Let G be a graph and H a subgraph of G. A backbone-k-coloring of (G, H) is a mapping f:V (G) → {1, 2, …, k} such that|f(u) -f(v)| ≥ 2 if uv ∈ E(H) and|f(u) -f(v)| ≥ 1 if uv ∈ E(G)\E(H). The backbone chromatic number of (G, H) denoted by χ_{b}(G, H) is the smallest integer k such that (G, H) has a backbone-k-coloring. In this paper, we prove that if G is either a connected triangle-free planar graph or a connected graph with mad(G) < 3, then there exists a spanning tree T of G such that χ_{b}(G, T) ≤ 4.
In equitable multiobjective optimization all the objectives are uniformly optimized, but in some cases the decision maker believes that some of them should be uniformly optimized according to the importance of objectives. To solve this problem in this paper, the original problem is decomposed into a collection of smaller subproblems, according to the decision maker, and the subproblems are solved by the concept of w^{r}-equitable efficiency, where w ∈ R_{+}^{m} is a weight vector. First some theoretical and practical aspects of Pw^{r}-equitably efficient solutions are discussed and by using the concept of Pw^{r}-equitable efficiency one model is presented to coordinate weakly w^{r}-equitable efficient solutions of subproblems. Then the concept of Pw^{∞}-equitable is introduced to generate subsets of equitably efficient solutions, which aims to offer a limited number of representative solutions to the decision maker.